Chung Sung-Jun/Getty Images(SEOUL, South Korea) -- Donald Trump became the first U.S. president to step into North Korea Sunday, reaching across the demarcation line to shake hands with North Korean leader Kim Jong Un and then, at Kim's invitation, stepping across the border and into North Korea -- in a historic moment Trump called "a great honor."

Kim, through a translator, called Trump's decision to meet with him a "courageous and determined act."

"I just want to thank you, it was very quick notice and I just want to thank you," Trump said.

"Good to see you again, I never expected to see you in this place," Kim said as they initially shook hands.

Both leaders spoke, standing side by side, before heading into a bilateral meeting in a nearby building.

"Tremendous positivity, really great things are happening" Trump said. "We met and we liked each other from day one and that was very important."

After Trump and Kim met for more than 40 minutes, they emerged together from the Freedom House -- along with Moon -- and walked side-by-side back to the demarcation line, where Trump and Moon bid Kim farewell.

Back inside Freedom House, Trump declared it a "great" and "legendary" day and said they agreed to formulate teams to restart active negotiations for a comprehensive agreement. Trump said Steve Biegun, U.S. special representative for North Korea, would lead the U.S. side.

"We just had a very, very good meeting with Chairman Kim and we’ve agreed that we’re going to designate a team, and the team will try and work out some deals, and again speed is not the object, we want to see if we can do a really comprehensive good deal."

"Nobody knows how things go, but certainly this was a great day. This was a very legendary, very historic day," Trump said.

"It will be more historic if something comes of it, something very important, but a lot has already come of it," Trump continued, pointing to the relationships that have been built through engaging directly with the North Koreans and claimed it was a "fiery mess" during the previous administration.

Prior to sitting down for their extended talk, the president said he would be inviting Kim to visit him at the White House.

"If it was not for the excellent relationship between us, it would not have been possible," Kim said during the bilateral.

Trump then spoke and first complimented the strength of Kim's voice.

"You hear the power of that voice, nobody's heard the voice before, he doesn't do news conferences, in case you haven't noticed, and this was a special moment," Trump said.

"This is an historic moment, the fact that we're meeting," Trump continued.

The president then thanked Kim for not turning down his invitation to meet at the border, because "if he didn't show up, the press was going to make us both look bad."

"You made us both look good and I appreciate it," Trump said.

"It was an honor that you asked me to step over that line, and I was proud to step over that line. I thought you might do that, I wasn't sure, but I was ready to do it, and I want to thank you, it was great, very historic," Trump said.

Trump arrived at the Korean demilitarized zone (DMZ) just before 2 a.m. Eastern time in a prelude to a historic meeting with Kim. Trump visited an observation tower, looking into the secluded North, where many U.S. presidents have stopped before.

But unlike previous presidents, Trump later met with Kim at Panmunjeom, the so-called Peace Village, on the border between the two countries and possibly cross over the line and become the first-ever president to visit North Korea.

Trump made brief comments from the overlook: "After our first summit, all the danger went away," Trump claimed. "I say that for the press, when they say there's been no difference. There's been a tremendous difference."

He visited U.S. troops at the border afterward, was given the gift of a jacket and signed the wall as has become tradition for presidents.

Just hours before, Trump announced he was set to travel to the demilitarized zone between North and South Korea at a joint press conference with South Korean President Moon Jae-in. Moon joined Trump in his visit to the border.

"I’ll be meeting with Chairman Kim I look forward to it very much. I look forward to seeing him, we’ve developed a very good relationship," Trump said at the press conference. "We understand each other. I do believe he understands me and I think I maybe understand him. And sometimes that can lead to very good things."

"I put out the word and he got back, and he wanted to do it from the beginning and so did I," Trump continued.

Expanding on his decision Saturday to extend a last-minute invite to Kim to meet him at the DMZ, Trump said the trip was "something I planned long ago, but had the idea yesterday, to maybe, say 'hello,' just shake and quickly say 'hello.'"

Asked about the possibility of a third summit, Trump said he'd like to see what happens Sunday before talking about another meeting.

"Let’s see what happens today before we start thinking about that," Trump said.

The president also claimed -- falsely -- that former President Barack Obama sought to meet with Kim and that he was rebuffed.

"The Obama administration was begging for a meeting, there were begging for meetings constantly, and Chairman Kim would not meet him," Trump claimed.

The president continued to express optimism about the state of relations with North Korea and insisted that important progress has been made through both of his previous summits with Kim.

"I'm not in a rush," Trump said. "If you're in a rush you get yourself in trouble."

On Sunday morning in South Korea, Trump said that Kim "very much wants to" meet, and that the two countries are "trying to work it out. Both want to do it."

"Very short, it would be very short, virtually a handshake," Trump said. "But that’s OK. A handshake means a lot."

Trump has even raised the possibility of stepping across the border into North Korea -- something no previous U.S. president has done.

"Sure, I would. I would. I'd feel very comfortable doing that. I would have no problem," Trump said earlier in his Asia trip.

The two leaders have met on two occasions. Their most recent meeting in February in Hanoi, Vietnam, failed to produce an agreement toward the goal of North Koreas' denuclearization.

Trump announced yesterday that he would be traveling to the DMZ during his visit to South Korea and issued an impromptu Twitter invitation to the North Korean leader to have a brief visit and share a handshake.

Since that time, a senior administration official said that the governments of the United States, North Korea and South Korea have been in communication to prepare for the prospective meeting.

In remarks Sunday morning at a breakfast with Korean business leaders, President Trump suggested that a meeting was likely to happen.